2m011 v01 ks2mathsmarkscheme 05012011 · 2011 ks2 mathematics tests mark schemes 1 ... the marking...

National curriculum assessments

2011

Ma Mathematics tests

Mark schemes Test A, Test B and mental mathematics

KEY STAGE

2LEVELS

3–5

Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk

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First published 2011

© Qualifications and Curriculum Development Agency 2011

ISBN 978-1-84962-791-7

Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced for the purpose of research, private study, criticism or review, or by educational institutions solely for educational purposes, without permission, provided full acknowledgement is given.

Printed in Great Britain by QCDA under the authority and superintendence of the Controller of Her Majesty’s Stationery Office and Queen’s Printer of Acts of Parliament.

Qualifications and Curriculum Development Agency 53-55 Butts RoadEarlsdon ParkCoventry CV1 3BH www.qcda.gov.uk


2011 KS2 Mathematics tests mark schemes

1

Marking the mathematics tests

As in 2010, external markers, employed by the external marking agencies under contract to QCDA, will mark the test papers. The markers will follow the mark schemes in this booklet, which is supplied to teachers for information.

This booklet contains the mark schemes for the levels 3–5 tests A, B and mental mathematics. Level threshold tables will be available from the Pupil results section of the QCDA website at www.qcda.gov.uk/tests from Tuesday 5 July 2011.

General guidance

The structure of the mark schemes

The marking information for each question is set out in the form of tables, which start on page 6 of this booklet.

The ‘Question’ column on the left-hand side of each table provides a quick reference to the question number and the question part.

The ‘Mark’ column indicates the total number of marks available for each question part. On some occasions the symbol may be shown in the ‘Mark’ column. The ‘U’ indicates that there is a Using and applying mathematics element in the question. The number, 1, shows the number of marks attributed to using and applying mathematics in this question.

The ‘Requirement’ column may include two types of information:

a statement of the requirements for the award of each mark, with an indication of whether credit can be given for correct working

examples of some different types of correct response.

The ‘Additional guidance’ column indicates alternative acceptable responses, and provides details of specific types of response which are unacceptable. Other guidance, such as the range of acceptable answers, is provided as necessary.

Additionally, for the mental mathematics test, general guidance on marking is given on page 18, followed by the marking information for each question.

Applying the mark schemes

In order to ensure consistency of marking, the most frequent procedural queries are listed on pages 2 and 3 along with the action the marker will take. This is followed by further guidance on pages 4 and 5 relating to the marking of questions that involve money, time and other measures. Unless otherwise specified in the mark scheme, markers will apply the following guidelines in all cases.


What if… Marking procedure

The pupil’s response is numerically or algebraically equivalent to the answer in the mark scheme.

Markers will award the mark unless the mark scheme states otherwise.

The pupil’s response does not match closely any of the examples given.

Markers will use their judgement in deciding whether the response corresponds with the statement of the requirements given in the ‘Requirement’ column. Reference will also be made to the additional guidance and, if there is still uncertainty, markers will contact the supervising marker.

The pupil has responded in a non-standard way.

Calculations, formulae and written responses do not have to be set out in any particular format. Pupils may provide evidence in any form as long as its meaning can be understood. Diagrams, symbols or words are acceptable for explanations or for indicating a response. Any correct method of setting out working, however idiosyncratic, will be accepted.

There appears to be a misreading affecting the working.

This is when the pupil misreads the information given in the question and uses different information without altering the original intention or difficulty level of the question. For each misread that occurs, one mark only will be deducted. In one-mark questions – 0 marks are awarded. In two-mark questions that have a method mark – 1 mark will be awarded if the correct method is correctly implemented with the misread number.

No answer is given in the expected place, but the correct answer is given elsewhere.

Where a pupil has shown understanding of the question, the mark(s) will be given. In particular, where a word or number response is expected, a pupil may meet the requirement by annotating a graph or labelling a diagram elsewhere in the question.

The pupil’s answer is correct but the wrong working is shown.

A correct response will always be marked as correct.

The response in the answer box is wrong, but the correct answer is shown in the working.

Where appropriate, detailed guidance will be given in the mark scheme, which markers will follow. If no guidance is given, markers will examine each case to decide whether:

� the incorrect answer is due to a transcription error

� the pupil has continued to give redundant extra working which does not contradict work already done

� the pupil has continued to give redundant extra working which does contradict work already done.

If so, the mark will be awarded.

If so, the mark will be awarded.

If so, the mark will not be awarded.

2

2011 KS2 Mathematics tests mark schemes General guidance



What if… Marking procedure

The correct response has been crossed out and not replaced.

Any legible crossed-out work that has not been replaced will be marked according to the mark scheme. If the work is replaced, then crossed-out work will not be considered.

More than one answer is given.

If all answers are correct (or a range of answers is given, all of which are correct), the mark will be awarded unless prohibited by the mark scheme. If both correct and incorrect responses are given, no mark will be awarded.

The answer is correct but, in a later part of the question, the pupil has contradicted this response.

A mark given for one part will not be disallowed for working or answers given in a different part, unless the mark scheme specifically states otherwise.

The pupil has drawn lines which do not meet at the correct point.

Markers will interpret the phrase ‘slight inaccuracies in drawing’ to mean ‘within or on a circle of radius 2mm with centre at the correct point’.

within the circleaccepted

on the circleaccepted

outside the circlenot accepted

Recording marks awarded on the test paper

In the margin there is a marking space alongside each question part.

For the mental mathematics test, the external marker will record ‘1’ for a correct response or ‘0’ otherwise.

For the written tests, the external marker will record one of the following in each marking space:

‘1’ for a correct response

‘0’ for an incorrect response

‘−‘ if no response is made.

A two-mark question which is correct will have ‘1’ entered in both marking spaces. A two-mark question which is incorrect, but which has sufficient evidence of working or method as required by the mark scheme, will have ‘1’ entered in the first marking space and ‘0’ in the second. Otherwise ‘0’ will be entered in both marking spaces, unless no response is made in which case ‘−’ will be entered in both marking spaces.

For the written tests, the total number of marks gained on each double page will be written in the space at the bottom of the right-hand page. For all of the tests, the total number of marks gained on each paper will be recorded on the front of the test paper.

Test A carries a total of 40 marks. Test B also carries a total of 40 marks. The mental mathematics test carries a total of 20 marks.

The 2011 key stage 2 mathematics tests and mark schemes were developed by the Test Development Team at Pearson Research and Assessment on behalf of QCDA.

3


4


Marking specific types of question – summary of additional guidance

Responses involving money

Accept Do not accept

Where the £ sign is given

for example:

£3.20, £7

£

£3.20 £7

£7.00

Any unambiguous indication of the correct amount, eg

£3.20p

£3 20 pence

£3 20

£3,20

£3-20

£3:20

Incorrect placement of pounds or pence, eg

£320

£320p

Incorrect placement of decimal point, or incorrect use or omission of 0, eg

£3.2

£3 200

£32 0

£3-2-0

Where the p sign is given

for example:

40p

p

40p


£0.40p

Incorrect or ambiguous use of pounds or pence, eg

0.40p

£40p

Where no sign is given

for example:

£3.20, 40p

£3.20 40p

320p £0.40


£3.20p £0.40p

£3 20 pence £.40p

£3 20 £.40

£3,20 40

£3-20 0.40

£3:20

3.20

320

3 pounds 20

Incorrect or ambiguous use of pounds or pence, eg

£320 £40

£320p £40p

£3.2 0.4

3.20p 0.40p



5

Responses involving time


A time interval

for example:

2 hours 30 minutes

2 hours 30 minutes

Any unambiguous, correct indication, eg

212 hours

2.5 hours

2h 30

2h 30 min

2 30

150 minutes

150

Digital electronic time, ie

2:30

Incorrect or ambiguous time interval, eg

2.30

2-30

2,30

230

2.3

2.3 hours

2.3h

2h 3

2.30 min

A specific time

for example:

8:40am, 17:20

8:40am

8:40

twenty to nine

Any unambiguous, correct indication, eg

08.40

8.40

0840

8 40

8-40

8,40

Unambiguous change to 12 or 24 hour clock, eg

17:20 as 5:20pm or 17:20pm

Incorrect time, eg

8.4am

8.40pm

Incorrect placement of separators, spaces, etc or incorrect use or omission of 0, eg

840

8:4:0

8.4

084

Responses involving measures


Where units are given (eg kg, m, l)

for example:

8.6kg

kg

8.6kg

Any unambiguous indication of the correct measurement, eg

8.60kg

8.6000kg

8kg 600g

Incorrect or ambiguous use of units, eg

8600kg

Note

If a pupil leaves the answer box empty but writes the answer elsewhere on the page, then that answer must be consistent with the units given in the answer box and the conditions listed above.

If a pupil changes the unit given in the answer box, then their answer must be equivalent to the correct answer using the unit they have chosen, unless otherwise indicated in the mark scheme.



6

Test A questions 1–8

Question Requirement Mark Additional guidance

1 845 1m

25

×

6

−

30

OR

5 × 8 − 40

1m

3a

3b

450

125

1m

1m

Accept an answer in the range 440 to 460 inclusive.

4 Five coins which total £1.60, ie

£1 20p 20p 10p 10p

OR

50p 50p 20p 20p 20p

OR

50p 50p 50p 5p 5p

1m

U1

Coins may be given in any order.

5 A AND D AND E 1m Letters may be given in any order.

6a

6b

54

63

1m

1m

7a

7b

7:55am

40 minutes

1m

1m

The answer is a specific time (see page 5 for guidance).

The answer is a time interval (see page 5 for guidance).

8 Award TWO marks for all three pairs of numbers correct as shown:

5 + 6

3 + 7

1 + 8

2 + 4

If the answer is incorrect, award ONE mark for two pairs of numbers correct.

Up to 2m

U1

Numbers within pairs may be given in either order.



7



9 Two numbers circled as shown:

255

650

735

900

995

1m Accept alternative unambiguous indications, eg numbers ticked, crossed or underlined.

10 Diagram completed as shown: 1m Accept inaccurate drawing provided the intention is clear.

11 Award TWO marks for all four symbols correct, as shown:

<

>

=

>

If the answer is incorrect, award ONE mark for three symbols correct.

Up to 2m

12 Award TWO marks for the correct answer of £3.05

If the answer is incorrect, award ONE mark for evidence of appropriate working, eg:

� £5.00 – £1.05 = £3.95

£7.00 – £3.95 = wrong answer

OR

� 7 – 5 = 2

2 + 1.05 = wrong answer

Up to 2m

Accept for ONE mark £305 OR £305p as evidence of appropriate working.

Working must be carried through to reach an answer for the award of ONE mark.

13a

13b

14

C

1m

1m Accept 5



8



14 Arrow drawn to 640, as shown:

0100900

grams200800

300700

400600500

1m Arrow should be closer to 640 than to 620 or 660

Accept any unambiguous indication of the correct point on the scale, including an arrow not originating from the centre of the dial.

Accept answer given on upper diagram provided no answer is given on lower diagram.

15 An explanation which recognises that the shaded area is equivalent to one-third, eg:

� ‘26 is shaded and that is equivalent to 13‘

� ‘2 out of 6 is the same as 1 out of 3’

� ‘2 out of 6’

� ‘26 is shaded and 46 is not shaded, which is the same as 13 shaded and 23 not shaded’

� ‘There are 3 squares, and 2 halves are shaded, and 2 halves make one whole’

� ‘The two shaded triangles are the same as one square and that is one out of three squares’

� ’1 square out of 3’

� ‘If you add the shaded parts together it makes one square’

�

1m

U1

No mark is awarded for circling ‘Yes’ alone.

Do not accept vague or incomplete explanations, eg:

� ’It’s equivalent to 13‘

� ‘13 is shaded and 23 is not shaded’

� ‘The two parts shaded add up to 13‘

� ‘Half of 2 squares are shaded’.

If ‘No’ is circled but a correct, unambiguous explanation is given, then award the mark.

16a

16b

16c

2

4

banana

1m

1m

1m

Do not accept nuts and fruit bar.

Accept unambiguous abbreviations or recognisable misspellings.

17 22.11 1m

18 4 1m Accept 21 AND 22 AND 23 AND 24



9



19a

19b

16

A whole number in the range 180 to 190 inclusive

1m

1m

2047 ÷ 100

= 0.47

AND

4.07 × 10 = 40.7

1m Numbers within calculations may be given in either order.

21 Award TWO marks for the correct answer of 17

If the answer is incorrect, award ONE mark for evidence of appropriate working which contains no more than ONE arithmetical error, eg:

� repeated addition/subtraction methods, eg

544 −320 10 × 32

224 −160 5 × 32

64 −64 2 × 32

0 wrong answer

� repeated halving, eg

544 ÷ 2 = 272 272 ÷ 2 = 136 136 ÷ 2 = 68 68 ÷ 2 = 34 34 ÷ 2 = wrong answer

� fraction method, eg54432 = 136

8 = 342 = wrong answer

� short division algorithm

wrong answer

32 5 4224

� long division algorithm

wrong answer

32 544320

224−224

0

Up to 2m

In all cases accept follow-through of ONE error in working.


Do not award any marks if the final answer is missing.

Variations on algorithms are acceptable, provided they represent a viable and complete method.

No mark is awarded for repeated addition/subtraction/halving the wrong number of times.

Short division methods must be supported by evidence of appropriate carrying figures to indicate use of a division algorithm.



10



22a

22b

Triangle drawn on the diagram as shown:

Quarter circle drawn on the diagram as shown above.

1m

1m

Accept inaccurate drawing provided the intention is clear.

Triangle must be shaded.

Accept inaccurate drawing provided the intention is clear.

The size of the quarter circle is not important, provided it does not touch the shaded rectangle.

Quarter circle need not be shaded.

23a

23b

13 for the x coordinate

15 for the y coordinate

1m

U1

1m

Accept unambiguous answers written on the diagram.

Accept unambiguous answers written on the diagram.

If the answer to 23a is 15 AND the answer to 23b is 13, then award ONE mark for 23b.



11

Test A question 24Markers will use a transparent overlay of this page to mark pupils’ answers to this question. A copy is enclosed.

6cm

8cm


24 Award TWO marks for a quadrilateral drawn with an angle in the range 73° to 77° inclusive AND length of sloping line in the range 9.1cm to 9.3cm inclusive (ie upper vertex of quadrilateral within inner box on diagram).

If the answer is incorrect, award ONE mark for:

� a completed quadrilateral drawn with an angle in the range 73° to 77° inclusive

OR

� a completed quadrilateral drawn with an angle in the range 72° to 78° inclusive AND length of sloping line in the range 9.0cm to 9.4cm inclusive.

Up to 2m Accept drawings where any side has been extended past a vertex.

Accept drawings which do not use the given 8cm base line, provided they have used a line with a length in the range 7.8cm to 8.2cm inclusive.

Accept for ONE mark drawings not using the given 8cm base line which have a base line outside the range 7.8cm to 8.2cm, provided they have an angle in the range 73° to 77° inclusive AND a sloping line in the range 9.1cm to 9.3cm inclusive.

Accept for ONE mark drawings of incomplete quadrilaterals, provided they have an angle in the range 73° to 77° inclusive AND a sloping line in the range 9.1cm to 9.3cm inclusive.



12

Test A question 25



If the answer is incorrect, award ONE mark for evidence of appropriate working, eg:

� 36 ÷ 3 = 12

36 ÷ 4 = 9

12 + 9 + 9 + 9 = wrong answer

OR

� 12

9

12 − 9 = 3

36 + 3 = wrong answer

Up to 2m

U1 Accept for ONE mark an answer of 42 supported by appropriate working, eg

36 + 3 + 3




13

Test B questions 1–5


1 Number circled as shown:

70

120

85

111

909

1m Accept alternative unambiguous indications, eg number ticked, crossed or underlined.

2 Calculations completed as shown:

10 + 30

=

40

20 + 30

=

50

1m Calculations may be given in either order.

The first two numbers within each calculation may be given in either order.

3 Award TWO marks for one line of symmetry positioned correctly on each diagram as shown:

If the answer is incorrect, award ONE mark for two diagrams completed correctly.

Up to 2m For the first diagram, accept slight inaccuracies in drawing (see page 3 for guidance).

For the second and third diagrams, accept inaccurate drawing provided the intention is clear.

4 Award TWO marks for four rows correct as shown:

If the answer is incorrect, award ONE mark for three rows correct.

Up to 2m Accept alternative unambiguous indications, eg û or Y.

5a

5b

2.5 OR 212

5

1m

1m



14



6a

6b

£63.25

28

1m

1m

7a

7b

112 OR 1.5

1

1m

1m

8 34 1m Accept equivalent fractions or decimals.

9 A AND D 1m Letters may be given in either order.

10a

10b

19

14

1m

1m

11 15 1m Accept equivalent fractions, eg 3

15

Accept 0.2 OR 20%

12 5 1m Do not accept a list of dates.


If the answer is incorrect, award ONE mark for evidence of appropriate method, eg:

� 30 × 50 = 1500

1500 ÷ 20

OR

� 30 × 50p = £15

5 20p coins make £1

5 × 15

OR

� 50p ÷ 20p = 2.5

30 × 2.5

Up to 2m

Answer need not be obtained for the award of ONE mark.



15



14a

14b

E

D

1m

1m

15 Award TWO marks for a multiple of 15 which is greater than 100, eg

105 OR 120 OR 135 OR 150 OR 300


� 90 93 96 99 102 105 108 …90 95 100 105 110 115 …

� 90 93 96 98 101 104 107 110 …90 95 100 105 110 115 …

� 15 30 45 60 75 80 95 110 125

� 3 × 5 × 20 OR 15 × 10

Up to 2m Accept more than one answer if all are correct.

Accept for ONE mark 30, 45, 60, 75 OR 90

Not spotting matching number (105)

One step size incorrect (96 to 98)

One step size incorrect (75 to 80)

Multiple greater than 100 but not calculated


16 Masses in order, as shown:

12 kg

800g

2kg

1 tonne

1m Accept answers with missing or incorrect units.

17

1 1 × 1 6

1m Numbers may be given in either order.

18 An explanation which gives a counter-example to illustrate that halving a number that ends in 8 does not always give a number ending in 4, eg:

� ’18 doesn’t work’

� ‘It could end in a 9’

� ‘Double 49 is 98’

� ’58 ÷ 2 = 29’

� ‘Half of 8 is 4 but half of 18 doesn’t end in 4’

� ’18, 28, 38, 48, 58, 68 – only half of them work’

� ‘It has to have an even number of 10s, like 28 or 88’

� ‘38’

1m

U1

No mark is awarded for circling ‘No’ alone.


� ‘Half of them don’t’

� ‘Half of 28 is 14’

� ‘Double 44 is 88’

If ‘Yes’ is circled but a correct, unambiguous explanation is given, then award the mark.



16





� 56 ÷ 7 = 8

2 × 8

OR

� 7 quarter-circles 2 triangles

14 quarter-circles 4 triangles

28 quarter-circles 8 triangles

56 quarter-circles …

Up to 2m


20a

20b

07:33

07:35

1m

1m



21 An explanation which recognises that there are two counters labelled 35 and only one counter labelled 45, eg:

� ‘For 35 there’s a white and a green, but for 45 there’s only a green’

� ‘There are two 35s and one 45’

� ‘There are twice as many 35s as 45s’

� ‘The only 45 is green’

� ‘There is only one 45’

� ‘White counters only go up to 40, so 35 would be more likely to win’

� 35 W

35 G

45 G

1m

U1

No mark is awarded for circling ‘Yes’ alone.


� ‘There are more counters below 40’

� ’45 is green’

� ‘White goes up to 40’

� ‘There are more greens’.

If ‘No’ is circled but a correct, unambiguous explanation is given, then award the mark.

22 Award TWO marks for all four letters in the correct order as shown:

99 J

29 G

–83 A

–15 E

44 H

If the answer is incorrect, award ONE mark for three letters correct.

Up to 2m



17



23 Diagram completed correctly as shown: 1m Accept slight inaccuracies in drawing (see page 3 for guidance).

24 60% 1m

U1

25 Award TWO marks for

Joe 10 AND

16

AND

Dev 9 AND

15

If the answer is incorrect, award ONE mark for:

� three numbers correctly attributed

OR

� 9 AND 10 AND 15 AND 16 with some or all attributed to the wrong child.

Up to 2m

U1Joe’s even numbers may be given in either order.

Dev’s odd numbers may be given in either order.

26 Award TWO marks for the correct answer of 3.6

If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg:

� 10 ÷ 0.05 = 200

200 × 1.8 = 360

360 ÷ 100

OR

� 20 5p coins make £1

200 5p coins make £10

200 × 0.018

Up to 2m Answer must be in metres for the award of TWO marks.

Accept for ONE mark 360 centimetres.

If the answer is incorrect, accept for ONE mark an answer of 36 multiplied by any power of 10 with no evidence of an incorrect method.




18

Mark scheme for the mental mathematics test

Applying the mark scheme

Please note that pupils will not be penalised if they record any information given in the question or show their working. Markers will ignore any annotation, even if in the answer space, and mark only the answer. Markers will accept an unambiguous answer written in the stimulus box, or elsewhere on the page.

Full mark scheme information is given on page 20. In addition, a ‘quick reference’ mark scheme is provided on page 19. This is presented in a similar format to the pupil’s answer sheet.

General guidance

The general guidance for marking the written tests also applies to marking the mental mathematics test. In addition, the following principles apply.

1. Unless stated otherwise in the mark scheme, accept answers written in words, or a combination of words and figures.

2. Where units are specified, they are given on the answer sheet. Pupils are not penalised for writing in the units again.

3. Where answers are required to be ringed, do not accept if more than one answer is ringed, unless it is clear which is the pupil’s intended answer. Accept also any other way of indicating the correct answer, eg underlining.


19

Mental mathematics 2011 quick reference mark scheme

Practice question

4 7.5 Accept 712

Time: 5 seconds

1 6204

2 28

5 65 mm

3 4250

7 180

Time: 10 seconds

6 £ 5

9 3 Accept 9r3 or remainder 3

8 75 min

14 200 Do not accept 200%

15 41

13 621

11 416

12 15 20 25 40 45

10 1.3

Time: 15 seconds

16 £1.10

18 114

20 0.999

17 18 cm

19 21



20

Mental mathematics questions 1–20


1 6204 1m Answer must be in figures.

2 28 1m

3 4250 1m

4 7.5 1m Accept 712

5 65mm 1m

6 £5 1m

7 180 1m

8 75 minutes 1m

9 3 1m Accept 9r3

Accept remainder 3

10 1.3 1m

11 416 1m

1215 20 25 40 45

1m Accept alternative unambiguous indications, eg underlining.

Do not accept if more than one answer is indicated unless the intention is clear.

13 621 1m

14 200 1m Do not accept 200%

15 41 1m

16 £1.10 1m

17 18cm 1m

18 114 1m

19 21 1m

20 0.999 1m


Qualifications and Curriculum Development Agency53−55 Butts RoadEarlsdon ParkCoventry CV1 3BHTelephone 0300 303 3013 Textphone 0300 303 3012 Fax: 0300 303 3014Email: [email protected]/tests

For more copiesQCDA Orderline, PO Box 29, Norwich NR3 1GNTel: 0300 303 3015 Fax: 0300 303 3016 Email: [email protected] Website: orderline.qcda.gov.ukQCDA/11/5231 (Mark schemes pack) 1070.01


2m011 v01 ks2mathsmarkscheme 05012011 · 2011 ks2 mathematics tests mark schemes 1 ... the marking...

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